Packages/settings

First, the most common packages for the following analyses have to be loaded and adjustments to the output are made.

# We load the helper-package pacman: 
if (!require("pacman")) install.packages("pacman")
if (!require("devtools")) install.packages("devtools")
if (!require("tidystats")) install_github("willemsleegers/tidystats")
# So that we don't have to type install.packages("PACKAGENAME"); library(PACKAGENAME)
# for every single package. Instead, we can just type p_load() and
# provide a list of desired packages in parentheses: 
pacman::p_load(tidyverse
       ,Routliers
       ,psych
       ,dplyr
       ,car
       ,TOSTER)

knitr::opts_chunk$set(message = FALSE,
                  warning = FALSE) # we don't want to see messages or warnings in the output

Importing csv

SPACE02_data <- read.csv2("data/SPACE02_data_wide_adjusted.csv", na="NA")

Data adjustment

New var “total_count” for data excl.

Total of the three different question forms.

SPACE02_data$total_count <- (SPACE02_data$recall_count + SPACE02_data$open.questions_count + SPACE02_data$transfer.questions_count)

Multi and practice as factors

SPACE02_data$practice <- as.factor(SPACE02_data$practice)
SPACE02_data$multi <- as.factor(SPACE02_data$multi)
SPACE02_data$total_count <- as.numeric(SPACE02_data$total_count)

New variable combining UVs

SPACE02_data$UVkomb <- interaction(SPACE02_data$multi, SPACE02_data$practice)
SPACE02_data$UVkomb <- as.factor(SPACE02_data$UVkomb)

Result is a variable UVkomb with four factors:
1. mono.massed µ1
2. mono.spaced µ2
3. multi.massed µ3
4. multi.spaced µ4

Data exclusion

Data exclusion was executed manually within the csv-file with the exception of the outliers.
- code here didn’t work, couldn’t find out why…

# "participated in the same study"
# Remove rows by a column value
# df[!(df$cyl == 6),]

SPACE02_data_adjusted <- SPACE02_data[!(SPACE02_data$participated.before == 'Ich habe schon einmal an DERSELBEN Studie teilgenommen.'),]
# 0 dataset removed

# external help "Ja"
# SPACE02_data_adjusted <- # SPACE02_data_adjusted[!(SPACE02_data_adjusted$external.help_s1 == 'yes'),]    

# SPACE02_data_adjusted <- # SPACE02_data_adjusted[!(SPACE02_data_adjusted$external.help_s2 == 'yes'),]

# external help
#SPACE02_data_adjusted <- SPACE02_data_adjusted[!(SPACE02_data_adjusted$external.help_post == 'yes'),]
# 9 datasets removed 114, 14, 24, 48, 139, 32, 39, 120, 128

# Diese Zeilen sollen entfernt werden
# drops <- c(114, 14, 24, 48, 139, 32, 39, 120, 128, 36, 43, 87)
# Zeilen löschen
# SPACE02_data_adjusted <- SPACE02_data_adjusted[-drops,]

# 12 datasets removed manually due to external help before import within the excel csv data - code here didn't work, couldn't find out why...

Detecting possible outliers

library(Routliers)
res1 <- outliers_mad(x = SPACE02_data_adjusted$total_count)
print(res1)

## Call:
## outliers_mad.default(x = SPACE02_data_adjusted$total_count)
## 
## Median:
## [1] 28
## 
## MAD:
## [1] 11.8608
## 
## Limits of acceptable range of values:
## [1] -7.5824 63.5824
## 
## Number of detected outliers
##  extremely low extremely high          total 
##              0              1              1

plot_outliers_mad(res1, x = SPACE02_data_adjusted$total_count)

# Dataset 41 removed (total_recall 67.0 > 63.58)
# Diese Zeilen sollen entfernt werden
drops_outlier <- c(41)
# Zeilen löschen
SPACE02_data_adjusted <- SPACE02_data_adjusted[-drops_outlier,]

Dataset names of Variables

SPACE02_data_adjusted
Variables:
UV1 = multi (mono, multi)
UV2 = practice (massed, spaced)
AV1 = recall_count
AV2 = open.questions_count
AV3 = transfer.questions_count

Deskriptive statistics

DescribeBy

# https://www.youtube.com/watch?v=ZJB_Ya964tY
describeBy(recall_count ~ multi + practice, mat=TRUE, data = SPACE02_data_adjusted)

	item	group1	group2	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
X11	1	mono	massed	1	44	18.46591	6.859383	18.75	18.40278	7.78365	4.0	39.5	35.5	0.3034930	0.2819421	1.0340909
X12	2	multi	massed	1	39	20.69231	5.293511	19.00	20.71212	6.67170	9.5	34.0	24.5	0.1366550	-0.3883242	0.8476401
X13	3	mono	spaced	1	41	19.17073	6.912497	19.00	18.86364	8.15430	5.0	38.5	33.5	0.4226669	0.0307775	1.0795507
X14	4	multi	spaced	1	40	22.28750	6.261285	22.50	22.43750	7.41300	4.0	36.0	32.0	-0.3271377	0.2411976	0.9899960

boxplot(recall_count ~ multi + practice, data = SPACE02_data_adjusted)

Summary

summary(SPACE02_data_adjusted)

##        ID           condition           multi      practice     gender         
##  Min.   :6155132   Length:164         mono :85   massed:83   Length:164        
##  1st Qu.:6217849   Class :character   multi:79   spaced:81   Class :character  
##  Median :6332452   Mode  :character                          Mode  :character  
##  Mean   :6312775                                                               
##  3rd Qu.:6383423                                                               
##  Max.   :6476953                                                               
##                                                                                
##       age          language          german.since   educational.attainment
##  Min.   :18.00   Length:164         Min.   : 7.00   Length:164            
##  1st Qu.:25.75   Class :character   1st Qu.:20.00   Class :character      
##  Median :39.00   Mode  :character   Median :26.00   Mode  :character      
##  Mean   :39.13                      Mean   :28.71                         
##  3rd Qu.:51.25                      3rd Qu.:30.00                         
##  Max.   :77.00                      Max.   :66.00                         
##                                     NA's   :143                           
##  delay_post_s1      delay_post_s2      delay_s2_s1        cognitive.effort
##  Length:164         Length:164         Length:164         Min.   :1.000   
##  Class :character   Class :character   Class :character   1st Qu.:4.750   
##  Mode  :character   Mode  :character   Mode  :character   Median :6.000   
##                                                           Mean   :5.817   
##                                                           3rd Qu.:7.250   
##                                                           Max.   :9.000   
##                                                                           
##  prior.knowledge    interest       jol_interim       jol_final     
##  Min.   : 0.00   Min.   :  0.00   Min.   :  0.00   Min.   :  0.00  
##  1st Qu.: 8.00   1st Qu.: 50.00   1st Qu.: 40.00   1st Qu.: 34.00  
##  Median :20.00   Median : 72.00   Median : 66.00   Median : 55.00  
##  Mean   :23.05   Mean   : 66.38   Mean   : 59.91   Mean   : 53.95  
##  3rd Qu.:33.25   3rd Qu.: 84.25   3rd Qu.: 77.25   3rd Qu.: 75.00  
##  Max.   :87.00   Max.   :100.00   Max.   :100.00   Max.   :100.00  
##                                                                    
##  pre.test_MC_no  pre.test_MC_acc   recall_count   recall_accuracy  
##  Min.   :0.000   Min.   :0.0000   Min.   : 4.00   Min.   :0.06154  
##  1st Qu.:2.000   1st Qu.:0.3333   1st Qu.:16.38   1st Qu.:0.25192  
##  Median :3.000   Median :0.5000   Median :19.50   Median :0.30000  
##  Mean   :2.957   Mean   :0.4929   Mean   :20.10   Mean   :0.30929  
##  3rd Qu.:4.000   3rd Qu.:0.6667   3rd Qu.:25.00   3rd Qu.:0.38462  
##  Max.   :6.000   Max.   :1.0000   Max.   :39.50   Max.   :0.60769  
##                                                                    
##  open.questions_count open.questions_acc transfer.questions_count
##  Min.   : 0.000       Min.   :0.0000     Min.   : 0.000          
##  1st Qu.: 2.500       1st Qu.:0.1923     1st Qu.: 2.000          
##  Median : 4.500       Median :0.3462     Median : 4.000          
##  Mean   : 4.302       Mean   :0.3309     Mean   : 4.198          
##  3rd Qu.: 6.000       3rd Qu.:0.4615     3rd Qu.: 6.000          
##  Max.   :12.000       Max.   :0.9231     Max.   :18.000          
##                                                                  
##  transfer.questions_acc imi.motiv.mean  imi.comp.mean   imi.press.mean
##  Min.   :0.00000        Min.   : 3.00   Min.   : 4.00   Min.   : 3.0  
##  1st Qu.:0.05556        1st Qu.: 8.00   1st Qu.:11.00   1st Qu.: 9.0  
##  Median :0.11111        Median :12.00   Median :15.00   Median :12.0  
##  Mean   :0.11662        Mean   :11.68   Mean   :14.12   Mean   :11.6  
##  3rd Qu.:0.16667        3rd Qu.:16.00   3rd Qu.:17.00   3rd Qu.:14.0  
##  Max.   :0.50000        Max.   :21.00   Max.   :22.00   Max.   :20.0  
##                                                                       
##  pft_solved.sum   pft_acc.of.solved    pft_acc           disturbed_s1    
##  Min.   : 4.000   Length:164         Length:164         Min.   : 0.0000  
##  1st Qu.: 7.000   Class :character   Class :character   1st Qu.: 0.0000  
##  Median : 9.000   Mode  :character   Mode  :character   Median : 0.0000  
##  Mean   : 8.506                                         Mean   : 0.9817  
##  3rd Qu.:10.000                                         3rd Qu.: 2.0000  
##  Max.   :10.000                                         Max.   :10.0000  
##                                                                          
##  concentration_s1 difficulties_s1    difficulties.note_s1 readability_s1    
##  Min.   : 0.000   Length:164         Length:164           Length:164        
##  1st Qu.: 7.000   Class :character   Class :character     Class :character  
##  Median : 9.000   Mode  :character   Mode  :character     Mode  :character  
##  Mean   : 8.079                                                             
##  3rd Qu.:10.000                                                             
##  Max.   :10.000                                                             
##                                                                             
##  external.help_s1     exam_s1          enjoy.reading_s1   reading.per.week_s1
##  Length:164         Length:164         Length:164         Min.   : 0.00      
##  Class :character   Class :character   Class :character   1st Qu.: 6.00      
##  Mode  :character   Mode  :character   Mode  :character   Median :14.50      
##                                                           Mean   :15.72      
##                                                           3rd Qu.:20.25      
##                                                           Max.   :56.00      
##                                                                              
##  fsk.reading1_s1    fsk.reading2_s1    fsk.reading3_s1     disturbed_s2  
##  Length:164         Length:164         Length:164         Min.   :0.000  
##  Class :character   Class :character   Class :character   1st Qu.:0.000  
##  Mode  :character   Mode  :character   Mode  :character   Median :0.000  
##                                                           Mean   :1.272  
##                                                           3rd Qu.:2.000  
##                                                           Max.   :8.000  
##                                                           NA's   :83     
##  concentration_s2 difficulties_s2    difficulties.note_s2 readability_s2    
##  Min.   : 0.000   Length:164         Length:164           Length:164        
##  1st Qu.: 6.000   Class :character   Class :character     Class :character  
##  Median : 9.000   Mode  :character   Mode  :character     Mode  :character  
##  Mean   : 7.519                                                             
##  3rd Qu.:10.000                                                             
##  Max.   :10.000                                                             
##  NA's   :83                                                                 
##  external.help_s2     exam_s2          enjoy.reading_s2   reading.per.week_s2
##  Length:164         Length:164         Length:164         Min.   : 1.0       
##  Class :character   Class :character   Class :character   1st Qu.: 8.0       
##  Mode  :character   Mode  :character   Mode  :character   Median :14.0       
##                                                           Mean   :15.1       
##                                                           3rd Qu.:20.0       
##                                                           Max.   :40.0       
##                                                           NA's   :83         
##  fsk.reading1_s2    fsk.reading2_s2    fsk.reading3_s2    disturbed_post  
##  Length:164         Length:164         Length:164         Min.   : 0.000  
##  Class :character   Class :character   Class :character   1st Qu.: 0.000  
##  Mode  :character   Mode  :character   Mode  :character   Median : 1.000  
##                                                           Mean   : 1.384  
##                                                           3rd Qu.: 2.000  
##                                                           Max.   :10.000  
##                                                                           
##  concentration_post difficulties_post  difficulties.note_post
##  Min.   : 0.000     Length:164         Length:164            
##  1st Qu.: 6.750     Class :character   Class :character      
##  Median : 9.000     Mode  :character   Mode  :character      
##  Mean   : 7.866                                              
##  3rd Qu.: 9.250                                              
##  Max.   :10.000                                              
##                                                              
##  external.help_post participated.before seriousness           notes          
##  Length:164         Length:164          Length:164         Length:164        
##  Class :character   Class :character    Class :character   Class :character  
##  Mode  :character   Mode  :character    Mode  :character   Mode  :character  
##                                                                              
##                                                                              
##                                                                              
##                                                                              
##   total_count             UVkomb  
##  Min.   : 4.00   mono.massed :44  
##  1st Qu.:21.00   multi.massed:39  
##  Median :27.75   mono.spaced :41  
##  Mean   :28.60   multi.spaced:40  
##  3rd Qu.:36.62                    
##  Max.   :63.00                    
##

Histogramm age

SPACE02_data_adjusted$gender <- as.factor(SPACE02_data_adjusted$gender)
hist(SPACE02_data_adjusted$age)

describe(SPACE02_data_adjusted$age)

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
X1	1	164	39.12805	14.44947	39	38.40909	19.2738	18	77	59	0.3029985	-1.007167	1.128314

Frequency tables groups

table(SPACE02_data_adjusted$multi, SPACE02_data_adjusted$practice)

##        
##         massed spaced
##   mono      44     41
##   multi     39     40

Mean/SD by groups/Variables

Total_count

For data-exclusion criteria

require("dplyr")
group_by(SPACE02_data_adjusted, multi, practice) %>%
  summarise(
    mean = mean(total_count, na.rm = TRUE),
    sd = sd(total_count, na.rm = TRUE)
  )

multi	practice	mean	sd
mono	massed	25.88636	11.631385
mono	spaced	26.90244	11.751712
multi	massed	29.41026	9.343497
multi	spaced	32.55000	10.853217

AV1 recall_count

require("dplyr")
group_by(SPACE02_data_adjusted, multi, practice) %>%
  summarise(
    mean = mean(recall_count, na.rm = TRUE),
    sd = sd(recall_count, na.rm = TRUE)
  )

multi	practice	mean	sd
mono	massed	18.46591	6.859383
mono	spaced	19.17073	6.912497
multi	massed	20.69231	5.293511
multi	spaced	22.28750	6.261285

AV2 open.questions_count

require("dplyr")
group_by(SPACE02_data_adjusted, multi, practice) %>%
  summarise(
    mean = mean(open.questions_count, na.rm = TRUE),
    sd = sd(open.questions_count, na.rm = TRUE)
  )

multi	practice	mean	sd
mono	massed	3.500000	2.345208
mono	spaced	4.268293	2.962468
multi	massed	4.192308	2.432281
multi	spaced	5.325000	2.489851

AV3 transfer.question_count

require("dplyr")
group_by(SPACE02_data_adjusted, multi, practice) %>%
  summarise(
    mean = mean(transfer.questions_count, na.rm = TRUE),
    sd = sd(transfer.questions_count, na.rm = TRUE)
  )

multi	practice	mean	sd
mono	massed	3.920454	3.211432
mono	spaced	3.463415	2.988290
multi	massed	4.525641	2.709507
multi	spaced	4.937500	2.842416

Boxplots

box plot with multiple groups +++++++++++++++++++++ plot total performance (“total_count”) by groups (“practice”) color box plot by a second group: “multi”

# if(!require(devtools)) install.packages("devtools")
# devtools::install_github("kassambara/ggpubr")
# install.packages("ggpubr")
library("ggpubr")

# boxplot with two factor variables multi and practice
boxplot(total_count ~ multi * practice, data=SPACE02_data_adjusted, frame = FALSE,
        col = c("#00AFBB", "#E7B800"), ylab="Retention performance", xlab = "Group")

## Standard error

describeBy(recall_count ~ multi + practice, data = SPACE02_data_adjusted, mat = TRUE)

	item	group1	group2	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
X11	1	mono	massed	1	44	18.46591	6.859383	18.75	18.40278	7.78365	4.0	39.5	35.5	0.3034930	0.2819421	1.0340909
X12	2	multi	massed	1	39	20.69231	5.293511	19.00	20.71212	6.67170	9.5	34.0	24.5	0.1366550	-0.3883242	0.8476401
X13	3	mono	spaced	1	41	19.17073	6.912497	19.00	18.86364	8.15430	5.0	38.5	33.5	0.4226669	0.0307775	1.0795507
X14	4	multi	spaced	1	40	22.28750	6.261285	22.50	22.43750	7.41300	4.0	36.0	32.0	-0.3271377	0.2411976	0.9899960

describeBy(open.questions_count ~ multi + practice, data = SPACE02_data_adjusted, mat = TRUE)

	item	group1	group2	vars	n	mean	sd	median	trimmed	mad	max	range	skew	kurtosis	se
X11	1	mono	massed	1	44	3.500000	2.345208	3.5	3.388889	2.96520	9.5	9.5	0.3554814	-0.6503569	0.3535534
X12	2	multi	massed	1	39	4.192308	2.432281	4.5	4.166667	2.22390	9.0	9.0	0.0644189	-0.8599603	0.3894767
X13	3	mono	spaced	1	41	4.268293	2.962468	4.0	4.060606	2.96520	12.0	12.0	0.5107148	-0.2871451	0.4626598
X14	4	multi	spaced	1	40	5.325000	2.489851	5.0	5.281250	2.59455	10.5	10.5	0.1083482	-0.3234491	0.3936800

describeBy(transfer.questions_count ~ multi + practice, data = SPACE02_data_adjusted, mat = TRUE)

	item	group1	group2	vars	n	mean	sd	median	trimmed	mad	max	range	skew	kurtosis	se
X11	1	mono	massed	1	44	3.920454	3.211432	3.50	3.611111	2.96520	18.0	18.0	1.8717678	6.0021612	0.4841415
X12	2	multi	massed	1	39	4.525641	2.709507	4.00	4.378788	2.22390	13.0	13.0	0.7828171	0.5675449	0.4338684
X13	3	mono	spaced	1	41	3.463415	2.988290	3.50	3.151515	2.22390	17.5	17.5	2.4176136	9.3081127	0.4666925
X14	4	multi	spaced	1	40	4.937500	2.842416	4.25	4.859375	2.59455	13.0	13.0	0.3926822	-0.1946393	0.4494254

# SPACE02_subset <- SPACE02_data_adjusted[,c("age", "multi", "recall_count", "open.questions_count", "transfer.questions_count")]

# SPACE02_subset_descr <- describeBy(SPACE02_subset, multi, skew = FALSE)
# print(SPACE02_subset_descr)

ANOVA + Testing assumptions

Metric dependent variables: yes, Likert-scales.
Levene-Test for homogeneity of variances
From the output above we can see that the p-value is not less than the significance level of 0.05.
This means that there is no evidence to suggest that the variance across groups is statistically significantly different.
Therefore, we can assume the homogeneity of variances in the different treatment groups.
Plot, normality:
As all the points fall approximately along this reference line, we can assume normality.
Shapiro-Wilk-Test, normality:
The conclusion above, is for anova1 supported by the Shapiro-Wilk test on the ANOVA residuals (W = 0.98383, p = 0.04721) which finds no indication that normality is violated.
For anova2 with W = 0.98014 and p = 0.01601 (below 0.05), the data significantly deviate from a normal distribution.

ANOVA all AVs

AV1anova <- aov(recall_count ~ multi + practice + multi*practice, data = SPACE02_data_adjusted)

AV2anova <- aov(open.questions_count ~ multi + practice + multi*practice, data = SPACE02_data_adjusted)

AV3anova <- aov(transfer.questions_count ~ multi + practice + multi*practice, data = SPACE02_data_adjusted)

summary(AV1anova)

##                 Df Sum Sq Mean Sq F value  Pr(>F)   
## multi            1    297  297.19   7.284 0.00771 **
## practice         1     53   52.68   1.291 0.25753   
## multi:practice   1      8    8.11   0.199 0.65633   
## Residuals      160   6528   40.80                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(AV2anova)

##                 Df Sum Sq Mean Sq F value Pr(>F)  
## multi            1   32.8   32.82   4.981 0.0270 *
## practice         1   36.5   36.50   5.541 0.0198 *
## multi:practice   1    1.4    1.36   0.206 0.6504  
## Residuals      160 1054.1    6.59                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

summary(AV3anova)

##                 Df Sum Sq Mean Sq F value Pr(>F)  
## multi            1   43.8   43.79   5.024 0.0264 *
## practice         1    0.1    0.06   0.007 0.9340  
## multi:practice   1    7.7    7.72   0.886 0.3480  
## Residuals      160 1394.7    8.72                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Effect size

library(DescTools)
EtaSq(AV1anova, type = 2, anova = FALSE)

##                     eta.sq eta.sq.part
## multi          0.042266260 0.042681076
## practice       0.007650407 0.008005322
## multi:practice 0.001177617 0.001240651

EtaSq(AV2anova, type = 2, anova = FALSE)

##                     eta.sq eta.sq.part
## multi          0.027701738 0.028710444
## practice       0.032453855 0.033470751
## multi:practice 0.001207597 0.001286907

EtaSq(AV3anova, type = 2, anova = FALSE)

##                      eta.sq  eta.sq.part
## multi          3.031456e-02 3.047746e-02
## practice       4.144346e-05 4.297412e-05
## multi:practice 5.339770e-03 5.506732e-03

apaTables

library(apaTables)
apa.2way.table(
  multi, practice, recall_count, SPACE02_data_adjusted, filename = NA, table.number = 3, show.conf.interval = TRUE, show.marginal.means = FALSE, landscape = TRUE)

## 
## 
## Table 3 
## 
## Means and standard deviations for recall_count as a function of a 2(multi) X 2(practice) design 
## 
##                      M       M_95%_CI   SD
##  practice:massed                          
##            multi                          
##             mono 18.47 [16.38, 20.55] 6.86
##            multi 20.69 [18.98, 22.41] 5.29
##                                           
##  practice:spaced                          
##            multi                          
##             mono 19.17 [16.99, 21.35] 6.91
##            multi 22.29 [20.29, 24.29] 6.26
## 
## Note. M and SD represent mean and standard deviation, respectively. 
## LL and UL indicate the lower and upper limits of the 
## 95% confidence interval for the mean, respectively. 
## The confidence interval is a plausible range of population means 
## that could have created a sample mean (Cumming, 2014).

apa.2way.table(
  multi, practice, open.questions_count, SPACE02_data_adjusted, filename = NA, table.number = 3, show.conf.interval = TRUE, show.marginal.means = FALSE, landscape = TRUE)

## 
## 
## Table 3 
## 
## Means and standard deviations for open.questions_count as a function of a 2(multi) X 2(practice) design 
## 
##                     M     M_95%_CI   SD
##  practice:massed                       
##            multi                       
##             mono 3.50 [2.79, 4.21] 2.35
##            multi 4.19 [3.40, 4.98] 2.43
##                                        
##  practice:spaced                       
##            multi                       
##             mono 4.27 [3.33, 5.20] 2.96
##            multi 5.33 [4.53, 6.12] 2.49
## 
## Note. M and SD represent mean and standard deviation, respectively. 
## LL and UL indicate the lower and upper limits of the 
## 95% confidence interval for the mean, respectively. 
## The confidence interval is a plausible range of population means 
## that could have created a sample mean (Cumming, 2014).

apa.2way.table(
  multi, practice, transfer.questions_count, SPACE02_data_adjusted, filename = NA, table.number = 3, show.conf.interval = TRUE, show.marginal.means = FALSE, landscape = TRUE)

## 
## 
## Table 3 
## 
## Means and standard deviations for transfer.questions_count as a function of a 2(multi) X 2(practice) design 
## 
##                     M     M_95%_CI   SD
##  practice:massed                       
##            multi                       
##             mono 3.92 [2.94, 4.90] 3.21
##            multi 4.53 [3.65, 5.40] 2.71
##                                        
##  practice:spaced                       
##            multi                       
##             mono 3.46 [2.52, 4.41] 2.99
##            multi 4.94 [4.03, 5.85] 2.84
## 
## Note. M and SD represent mean and standard deviation, respectively. 
## LL and UL indicate the lower and upper limits of the 
## 95% confidence interval for the mean, respectively. 
## The confidence interval is a plausible range of population means 
## that could have created a sample mean (Cumming, 2014).

Levene-Test all AV

library(car)
leveneTest(recall_count ~ multi*practice, data= SPACE02_data_adjusted)

	Df	F value	Pr(>F)
group	3	0.820964	0.4840765
	160	NA	NA

leveneTest(open.questions_count ~ multi*practice, data= SPACE02_data_adjusted)

	Df	F value	Pr(>F)
group	3	0.9657767	0.4104437
	160	NA	NA

leveneTest(transfer.questions_count ~ multi*practice, data= SPACE02_data_adjusted)

	Df	F value	Pr(>F)
group	3	0.324261	0.8078188
	160	NA	NA

# p-Wert nicht signifikant ---> 0-Hypothese wird nicht verworfen (lautet: Varianzhomogenität liegt vor)
# 0-Hypothese muss beibehalten werden bei p>0.05

Normal distribution of residuals

plot(AV1anova, 2)

# summary(AV1anova)

plot(AV2anova, 2)

# summary(AV2anova)

plot(AV3anova, 2)

# summary(AV3anova)

Interaction plot

AV1

interaction.plot(SPACE02_data_adjusted$multi, SPACE02_data_adjusted$practice, SPACE02_data_adjusted$recall_count,
                 main="Interaction diagram free recall question",
                 ylim = c(18, 23),
                 lwd=2, 
                 ylab = "Mean", 
                 xlab = "Material", 
                 trace.label = "Practice",
                 type = "b", 
                 col=c("blue","black"), 
                 pch = c(17,19), 
                 fixed = TRUE)

AV2

interaction.plot(SPACE02_data_adjusted$multi, SPACE02_data_adjusted$practice, SPACE02_data_adjusted$open.questions_count,
                 main="Interaction diagram open questions", col=c("red", "blue", "green"), lwd=2, ylab = "Mean", xlab = "Material", trace.label = "Practice")

AV3

interaction.plot(SPACE02_data_adjusted$multi, SPACE02_data_adjusted$practice, SPACE02_data_adjusted$transfer.questions_count,
                 main="Interaction diagram transfer questions", col=c("red", "blue", "green"), lwd=2, ylab = "Mean", xlab = "Material", trace.label = "Practice")

Boxplots

SPACE02_data_adjusted %>%
  ggplot(aes(x = condition, y = recall_count)) + 
  geom_boxplot() +
  theme_bw()

SPACE02_data_adjusted %>%
  ggplot(aes(x = condition, y = open.questions_count)) + 
  geom_boxplot() +
  theme_bw()

SPACE02_data_adjusted %>%
  ggplot(aes(x = condition, y = transfer.questions_count)) + 
  geom_boxplot() +
  theme_bw()

AV1

error.bars.by(recall_count ~ practice + multi + practice*multi, data = SPACE02_data_adjusted, 
              ylab = "Retention performance", 
              eyes = F, 
              within = F, 
              main = "Interaction diagram free recall question", 
              xlab="Material", 
              v.lab = c("Mono", "Multi"), 
              lty = c(2,2), 
              lines = TRUE, 
              ylim = c(15, 25))
              legend("topleft", 
                     c("Spaced", "Massed"), 
                     lty = FALSE)

              colors=c("blue","black")



boxplot(recall_count ~ practice + multi, data = SPACE02_data_adjusted, 
        ann = TRUE,
        main = "Free recall question",
        xlab = "Group",
        ylab = "Retention performance")

boxplot(open.questions_count ~ practice + multi, data = SPACE02_data_adjusted, 
        ann = TRUE,
        main = "Open questions",
        xlab = "Group",
        ylab = "Retention performance")

boxplot(transfer.questions_count ~ practice + multi, data = SPACE02_data_adjusted, 
        ann = TRUE,
        main = "Transfer questions",
        xlab = "Group",
        ylab = "Retention performance")

AV2

error.bars.by(open.questions_count ~ practice + multi + practice*multi, data = SPACE02_data_adjusted, eyes = F, within = F, main = "Interaction diagram", xlab="Multi", v.lab = c("Multi", "Mono"), lty = c(1,2), ylim = c(2, 6.5))
legend("topleft", c("Massed", "Spaced"), lty = c(1,2))

boxplot(open.questions_count ~ practice + multi, data = SPACE02_data_adjusted)

AV3

error.bars.by(transfer.questions_count ~ practice + multi + practice*multi, data = SPACE02_data_adjusted, eyes = F, within = F, main = "Interaction diagram", xlab="Multi", v.lab = c("Multi", "Mono"), lty = c(1,2), ylim = c(2.5, 6))
legend("topleft", c("Massed", "Spaced"), lty = c(1,2))

boxplot(transfer.questions_count ~ practice + multi, data = SPACE02_data_adjusted)

Contrasts

Package lsmeans

Source:
https://stats.stackexchange.com/questions/190427/contrasts-in-anova-in-r

library(lsmeans)
(lsmAV1 <- lsmeans(AV1anova, ~ multi + practice))

##  multi practice lsmean    SE  df lower.CL upper.CL
##  mono  massed     18.5 0.963 160     16.6     20.4
##  multi massed     20.7 1.023 160     18.7     22.7
##  mono  spaced     19.2 0.998 160     17.2     21.1
##  multi spaced     22.3 1.010 160     20.3     24.3
## 
## Confidence level used: 0.95

(lsmAV2 <- lsmeans(AV2anova, ~ multi + practice))

##  multi practice lsmean    SE  df lower.CL upper.CL
##  mono  massed     3.50 0.387 160     2.74     4.26
##  multi massed     4.19 0.411 160     3.38     5.00
##  mono  spaced     4.27 0.401 160     3.48     5.06
##  multi spaced     5.33 0.406 160     4.52     6.13
## 
## Confidence level used: 0.95

(lsmAV3 <- lsmeans(AV3anova, ~ multi + practice))

##  multi practice lsmean    SE  df lower.CL upper.CL
##  mono  massed     3.92 0.445 160     3.04     4.80
##  multi massed     4.53 0.473 160     3.59     5.46
##  mono  spaced     3.46 0.461 160     2.55     4.37
##  multi spaced     4.94 0.467 160     4.02     5.86
## 
## Confidence level used: 0.95

Defining contrasts

contr1.1 <- list("Spacing alone" = c(-1, 0, 1, 0))
contr2.1 <- list("Multimedia alone" = c(-1, 1, 0, 0))
contr3.1 <- list("Interaction-Spacing" = c(0, 0, -1, 1))
contr3.2 <- list("Interaction-Multimedia" = c(0, -1, 0, 1))

AV1

contrast(lsmAV1, contr1.1)

##  contrast      estimate   SE  df t.ratio p.value
##  Spacing alone    0.705 1.39 160   0.508  0.6119

contrast(lsmAV1, contr2.1)

##  contrast         estimate  SE  df t.ratio p.value
##  Multimedia alone     2.23 1.4 160   1.585  0.1150

contrast(lsmAV1, contr3.1)

##  contrast            estimate   SE  df t.ratio p.value
##  Interaction-Spacing     3.12 1.42 160   2.196  0.0296

contrast(lsmAV1, contr3.2)

##  contrast               estimate   SE  df t.ratio p.value
##  Interaction-Multimedia      1.6 1.44 160   1.110  0.2688

AV2

contrast(lsmAV2, contr1.1)

##  contrast      estimate    SE  df t.ratio p.value
##  Spacing alone    0.768 0.557 160   1.379  0.1698

contrast(lsmAV2, contr2.1)

##  contrast         estimate    SE  df t.ratio p.value
##  Multimedia alone    0.692 0.565 160   1.226  0.2219

contrast(lsmAV2, contr3.1)

##  contrast            estimate   SE  df t.ratio p.value
##  Interaction-Spacing     1.06 0.57 160   1.852  0.0658

contrast(lsmAV2, contr3.2)

##  contrast               estimate    SE  df t.ratio p.value
##  Interaction-Multimedia     1.13 0.578 160   1.961  0.0516

AV3

contrast(lsmAV3, contr1.1)

##  contrast      estimate    SE  df t.ratio p.value
##  Spacing alone   -0.457 0.641 160  -0.713  0.4768

contrast(lsmAV3, contr2.1)

##  contrast         estimate    SE  df t.ratio p.value
##  Multimedia alone    0.605 0.649 160   0.932  0.3527

contrast(lsmAV3, contr3.1)

##  contrast            estimate    SE  df t.ratio p.value
##  Interaction-Spacing     1.47 0.656 160   2.247  0.0260

contrast(lsmAV3, contr3.2)

##  contrast               estimate    SE  df t.ratio p.value
##  Interaction-Multimedia    0.412 0.664 160   0.620  0.5362

H1 Equivalence test Spacing effect

For calculating/reading convenience descriptive statistics for the variables appears first with every H/AV-combination

Descriptive statistics AV1

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_recall_count = mean(recall_count), sd_recall_count = sd(recall_count), n = n(), na.rm = TRUE)

UVkomb	mean_recall_count	sd_recall_count	n	na.rm
mono.massed	18.46591	6.859383	44	TRUE
multi.massed	20.69231	5.293511	39	TRUE
mono.spaced	19.17073	6.912497	41	TRUE
multi.spaced	22.28750	6.261285	40	TRUE

H1-AV1

massed/text-spaced/text for recall_count

library(TOSTER)
TOSTtwo(m1 = 18.46591, m2 = 19.17073, sd1 = 6.859383, sd2 = 6.912498, n1 = 44, n2 = 41, low_eqbound_d = -0.25, high_eqbound_d = 0.25, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 0.68    p-value lower bound: 0.249
## t-value upper bound: -1.62   p-value upper bound: 0.054
## degrees of freedom : 82.48
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.25 
## high eqbound: 0.25
## 
## Equivalence bounds (raw scores):
## low eqbound: -1.7215 
## high eqbound: 1.7215
## 
## TOST confidence interval:
## lower bound 90% CI: -3.192
## upper bound 90% CI:  1.782
## 
## NHST confidence interval:
## lower bound 95% CI: -3.678
## upper bound 95% CI:  2.269
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(82.48) = 0.680, p = 0.249, given equivalence bounds of -1.721 and 1.721 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(82.48) = -0.471, p = 0.639, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Descriptive statistics AV2

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_open.questions_count = mean(open.questions_count), sd_open.questions_count = sd(open.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_open.questions_count	sd_open.questions_count	n	na.rm
mono.massed	3.500000	2.345208	44	TRUE
multi.massed	4.192308	2.432281	39	TRUE
mono.spaced	4.268293	2.962468	41	TRUE
multi.spaced	5.325000	2.489851	40	TRUE

H1-AV2

massed/text-spaced/text for open questions

library(TOSTER)
TOSTtwo(m1 = 3.500000, m2 = 4.268293, sd1 = 2.345208, sd2 = 2.962468, n1 = 44, n2 = 41, low_eqbound_d = -0.25, high_eqbound_d = 0.25, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: -0.172  p-value lower bound: 0.568
## t-value upper bound: -2.47   p-value upper bound: 0.008
## degrees of freedom : 76.19
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.25 
## high eqbound: 0.25
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.6679 
## high eqbound: 0.6679
## 
## TOST confidence interval:
## lower bound 90% CI: -1.738
## upper bound 90% CI:  0.201
## 
## NHST confidence interval:
## lower bound 95% CI: -1.928
## upper bound 95% CI:  0.391
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(76.19) = -0.172, p = 0.568, given equivalence bounds of -0.668 and 0.668 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(76.19) = -1.319, p = 0.191, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Descriptive statistics AV3

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_transfer.questions_count = mean(transfer.questions_count), sd_transfer.questions_count = sd(transfer.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_transfer.questions_count	sd_transfer.questions_count	n	na.rm
mono.massed	3.920454	3.211432	44	TRUE
multi.massed	4.525641	2.709507	39	TRUE
mono.spaced	3.463415	2.988290	41	TRUE
multi.spaced	4.937500	2.842416	40	TRUE

H1-AV3

massed/text-massed/multimedia for open questions

library(TOSTER)
TOSTtwo(m1 = 3.920455, m2 = 3.463415, sd1 = 3.211432, sd2 = 2.988290, n1 = 44, n2 = 41, low_eqbound_d = -0.2, high_eqbound_d = 0.2, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 1.60    p-value lower bound: 0.056
## t-value upper bound: -0.243  p-value upper bound: 0.404
## degrees of freedom : 83
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.2 
## high eqbound: 0.2
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.6204 
## high eqbound: 0.6204
## 
## TOST confidence interval:
## lower bound 90% CI: -0.662
## upper bound 90% CI:  1.576
## 
## NHST confidence interval:
## lower bound 95% CI: -0.88
## upper bound 95% CI:  1.795
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(83) = -0.243, p = 0.404, given equivalence bounds of -0.620 and 0.620 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(83) = 0.680, p = 0.499, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

H2 Equivalence test Multimedia effect

Descriptive statistics AV1

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_recall_count = mean(recall_count), sd_recall_count = sd(recall_count), n = n(), na.rm = TRUE)

UVkomb	mean_recall_count	sd_recall_count	n	na.rm
mono.massed	18.46591	6.859383	44	TRUE
multi.massed	20.69231	5.293511	39	TRUE
mono.spaced	19.17073	6.912497	41	TRUE
multi.spaced	22.28750	6.261285	40	TRUE

H2-AV1

massed/text-massed/multimedia for recall_count

library(TOSTER)
TOSTtwo(m1 = 18.46591, m2 = 20.69231, sd1 = 6.859383, sd2 = 5.293511, n1 = 44, n2 = 39, low_eqbound_d = -0.25, high_eqbound_d = 0.25, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: -0.52   p-value lower bound: 0.698
## t-value upper bound: -2.81   p-value upper bound: 0.003
## degrees of freedom : 79.56
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.25 
## high eqbound: 0.25
## 
## Equivalence bounds (raw scores):
## low eqbound: -1.5317 
## high eqbound: 1.5317
## 
## TOST confidence interval:
## lower bound 90% CI: -4.452
## upper bound 90% CI:  -0.001
## 
## NHST confidence interval:
## lower bound 95% CI: -4.888
## upper bound 95% CI:  0.435
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(79.56) = -0.520, p = 0.698, given equivalence bounds of -1.532 and 1.532 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(79.56) = -1.665, p = 0.0998, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Descriptive statistics AV2

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_open.questions_count = mean(open.questions_count), sd_open.questions_count = sd(open.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_open.questions_count	sd_open.questions_count	n	na.rm
mono.massed	3.500000	2.345208	44	TRUE
multi.massed	4.192308	2.432281	39	TRUE
mono.spaced	4.268293	2.962468	41	TRUE
multi.spaced	5.325000	2.489851	40	TRUE

H2-AV2

massed/text-massed/multimedia for open questions

library(TOSTER)
TOSTtwo(m1 = 3.500000, m2 = 4.192308, sd1 = 2.345208, sd2 = 2.432281, n1 = 44, n2 = 39, low_eqbound_d = -0.25, high_eqbound_d = 0.25, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: -0.181  p-value lower bound: 0.571
## t-value upper bound: -2.45   p-value upper bound: 0.008
## degrees of freedom : 79.01
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.25 
## high eqbound: 0.25
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.5973 
## high eqbound: 0.5973
## 
## TOST confidence interval:
## lower bound 90% CI: -1.568
## upper bound 90% CI:  0.183
## 
## NHST confidence interval:
## lower bound 95% CI: -1.739
## upper bound 95% CI:  0.355
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(79.01) = -0.181, p = 0.571, given equivalence bounds of -0.597 and 0.597 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(79.01) = -1.316, p = 0.192, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Descriptive statistics AV3

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_transfer.questions_count = mean(transfer.questions_count), sd_transfer.questions_count = sd(transfer.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_transfer.questions_count	sd_transfer.questions_count	n	na.rm
mono.massed	3.920454	3.211432	44	TRUE
multi.massed	4.525641	2.709507	39	TRUE
mono.spaced	3.463415	2.988290	41	TRUE
multi.spaced	4.937500	2.842416	40	TRUE

H2-AV3

massed/text-massed/multimedia for transfer questions

library(TOSTER)
TOSTtwo(m1 = 3.920455, m2 = 4.525641, sd1 = 3.211432, sd2 = 2.709507, n1 = 44, n2 = 39, low_eqbound_d = -0.2, high_eqbound_d = 0.2, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: -0.0169     p-value lower bound: 0.507
## t-value upper bound: -1.84   p-value upper bound: 0.034
## degrees of freedom : 80.82
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.2 
## high eqbound: 0.2
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.5942 
## high eqbound: 0.5942
## 
## TOST confidence interval:
## lower bound 90% CI: -1.687
## upper bound 90% CI:  0.477
## 
## NHST confidence interval:
## lower bound 95% CI: -1.899
## upper bound 95% CI:  0.688
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(80.82) = -0.0169, p = 0.507, given equivalence bounds of -0.594 and 0.594 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(80.82) = -0.931, p = 0.355, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

H3 Interaction

Descriptive statistics AV1

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_recall_count = mean(recall_count), sd_recall_count = sd(recall_count), n = n(), na.rm = TRUE)

UVkomb	mean_recall_count	sd_recall_count	n	na.rm
mono.massed	18.46591	6.859383	44	TRUE
multi.massed	20.69231	5.293511	39	TRUE
mono.spaced	19.17073	6.912497	41	TRUE
multi.spaced	22.28750	6.261285	40	TRUE

H3.1-AV1

spaced/multimedia-spaced/text for recall_count

library(TOSTER)
TOSTtwo(m1 = 22.28750, m2 = 19.17073, sd1 = 6.261285, sd2 = 6.912498, n1 = 40, n2 = 41, low_eqbound_d = -0.25, high_eqbound_d = 0.25, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 3.25    p-value lower bound: 0.0008
## t-value upper bound: 1.00    p-value upper bound: 0.840
## degrees of freedom : 78.57
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.25 
## high eqbound: 0.25
## 
## Equivalence bounds (raw scores):
## low eqbound: -1.6487 
## high eqbound: 1.6487
## 
## TOST confidence interval:
## lower bound 90% CI: 0.679
## upper bound 90% CI:  5.555
## 
## NHST confidence interval:
## lower bound 95% CI: 0.201
## upper bound 95% CI:  6.033
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(78.57) = 1.002, p = 0.840, given equivalence bounds of -1.649 and 1.649 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was significant, t(78.57) = 2.128, p = 0.0365, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically different from zero and statistically not equivalent to zero.

Descriptive statistics AV2

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_open.questions_count = mean(open.questions_count), sd_open.questions_count = sd(open.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_open.questions_count	sd_open.questions_count	n	na.rm
mono.massed	3.500000	2.345208	44	TRUE
multi.massed	4.192308	2.432281	39	TRUE
mono.spaced	4.268293	2.962468	41	TRUE
multi.spaced	5.325000	2.489851	40	TRUE

H3.1-AV2

spaced/multimedia-spaced/text for open questions

library(TOSTER)
TOSTtwo(m1 = 5.325000, m2 = 4.268293, sd1 = 2.489851, sd2 = 2.962468, n1 = 40, n2 = 41, low_eqbound_d = -0.25, high_eqbound_d = 0.25, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 2.87    p-value lower bound: 0.003
## t-value upper bound: 0.613   p-value upper bound: 0.729
## degrees of freedom : 77.32
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.25 
## high eqbound: 0.25
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.6841 
## high eqbound: 0.6841
## 
## TOST confidence interval:
## lower bound 90% CI: 0.045
## upper bound 90% CI:  2.068
## 
## NHST confidence interval:
## lower bound 95% CI: -0.153
## upper bound 95% CI:  2.266
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(77.32) = 0.613, p = 0.729, given equivalence bounds of -0.684 and 0.684 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(77.32) = 1.739, p = 0.0859, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Descriptive statistics AV3

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_transfer.questions_count = mean(transfer.questions_count), sd_transfer.questions_count = sd(transfer.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_transfer.questions_count	sd_transfer.questions_count	n	na.rm
mono.massed	3.920454	3.211432	44	TRUE
multi.massed	4.525641	2.709507	39	TRUE
mono.spaced	3.463415	2.988290	41	TRUE
multi.spaced	4.937500	2.842416	40	TRUE

H3.1-AV3

spaced/multimedia-spaced/text for transfer questions

library(TOSTER)
TOSTtwo(m1 = 4.937500, m2 = 3.463415, sd1 = 2.842416, sd2 = 2.988290, n1 = 40, n2 = 41, low_eqbound_d = -0.2, high_eqbound_d = 0.2, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 3.18    p-value lower bound: 0.001
## t-value upper bound: 1.37    p-value upper bound: 0.913
## degrees of freedom : 78.95
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.2 
## high eqbound: 0.2
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.5833 
## high eqbound: 0.5833
## 
## TOST confidence interval:
## lower bound 90% CI: 0.396
## upper bound 90% CI:  2.552
## 
## NHST confidence interval:
## lower bound 95% CI: 0.184
## upper bound 95% CI:  2.764
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(78.95) = 1.375, p = 0.913, given equivalence bounds of -0.583 and 0.583 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was significant, t(78.95) = 2.275, p = 0.0256, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically different from zero and statistically not equivalent to zero.

Descriptive statistics AV1

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_recall_count = mean(recall_count), sd_recall_count = sd(recall_count), n = n(), na.rm = TRUE)

UVkomb	mean_recall_count	sd_recall_count	n	na.rm
mono.massed	18.46591	6.859383	44	TRUE
multi.massed	20.69231	5.293511	39	TRUE
mono.spaced	19.17073	6.912497	41	TRUE
multi.spaced	22.28750	6.261285	40	TRUE

H3.2-AV1

library(TOSTER)
TOSTtwo(m1 = 22.28750, m2 = 20.69231, sd1 = 6.261285, sd2 = 5.293511, n1 = 40, n2 = 39, low_eqbound_d = -0.2, high_eqbound_d = 0.2, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 2.11    p-value lower bound: 0.019
## t-value upper bound: 0.334   p-value upper bound: 0.630
## degrees of freedom : 75.5
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.2 
## high eqbound: 0.2
## 
## Equivalence bounds (raw scores):
## low eqbound: -1.1595 
## high eqbound: 1.1595
## 
## TOST confidence interval:
## lower bound 90% CI: -0.575
## upper bound 90% CI:  3.766
## 
## NHST confidence interval:
## lower bound 95% CI: -1.001
## upper bound 95% CI:  4.191
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(75.5) = 0.334, p = 0.630, given equivalence bounds of -1.160 and 1.160 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(75.5) = 1.224, p = 0.225, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Descriptive statistics AV2

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_open.questions_count = mean(open.questions_count), sd_open.questions_count = sd(open.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_open.questions_count	sd_open.questions_count	n	na.rm
mono.massed	3.500000	2.345208	44	TRUE
multi.massed	4.192308	2.432281	39	TRUE
mono.spaced	4.268293	2.962468	41	TRUE
multi.spaced	5.325000	2.489851	40	TRUE

H3.2-AV2

spaced/multimedia-massed/multimedia for open questions

library(TOSTER)
TOSTtwo(m1 = 5.325000, m2 = 4.192308, sd1 = 2.489851, sd2 = 2.432281, n1 = 40, n2 = 39, low_eqbound_d = -0.2, high_eqbound_d = 0.2, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 2.93    p-value lower bound: 0.002
## t-value upper bound: 1.16    p-value upper bound: 0.874
## degrees of freedom : 77
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.2 
## high eqbound: 0.2
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.4922 
## high eqbound: 0.4922
## 
## TOST confidence interval:
## lower bound 90% CI: 0.211
## upper bound 90% CI:  2.055
## 
## NHST confidence interval:
## lower bound 95% CI: 0.03
## upper bound 95% CI:  2.235
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(77) = 1.156, p = 0.874, given equivalence bounds of -0.492 and 0.492 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was significant, t(77) = 2.045, p = 0.0442, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically different from zero and statistically not equivalent to zero.

Descriptive statistics AV3

library(dplyr)
by_UVkomb <- group_by(SPACE02_data_adjusted, UVkomb)
summarise(by_UVkomb, mean_transfer.questions_count = mean(transfer.questions_count), sd_transfer.questions_count = sd(transfer.questions_count), n = n(), na.rm = TRUE)

UVkomb	mean_transfer.questions_count	sd_transfer.questions_count	n	na.rm
mono.massed	3.920454	3.211432	44	TRUE
multi.massed	4.525641	2.709507	39	TRUE
mono.spaced	3.463415	2.988290	41	TRUE
multi.spaced	4.937500	2.842416	40	TRUE

H3.2-AV3

spaced/multimedia-massed/multimedia for transfer questions

library(TOSTER)
TOSTtwo(m1 = 4.937500, m2 = 4.525641, sd1 = 2.842416, sd2 = 2.709507, n1 = 40, n2 = 39, low_eqbound_d = -0.2, high_eqbound_d = 0.2, alpha = 0.05, var.equal = FALSE)

## TOST results:
## t-value lower bound: 1.55    p-value lower bound: 0.063
## t-value upper bound: -0.23   p-value upper bound: 0.409
## degrees of freedom : 76.96
## 
## Equivalence bounds (Cohen's d):
## low eqbound: -0.2 
## high eqbound: 0.2
## 
## Equivalence bounds (raw scores):
## low eqbound: -0.5554 
## high eqbound: 0.5554
## 
## TOST confidence interval:
## lower bound 90% CI: -0.628
## upper bound 90% CI:  1.452
## 
## NHST confidence interval:
## lower bound 95% CI: -0.832
## upper bound 95% CI:  1.656
## 
## Equivalence Test Result:
## The equivalence test was non-significant, t(76.96) = -0.230, p = 0.409, given equivalence bounds of -0.555 and 0.555 (on a raw scale) and an alpha of 0.05.
## Null Hypothesis Test Result:
## The null hypothesis test was non-significant, t(76.96) = 0.659, p = 0.512, given an alpha of 0.05.
## Based on the equivalence test and the null-hypothesis test combined, we can conclude that the observed effect is statistically not different from zero and statistically not equivalent to zero.

Data Analysis SPACE02 - BA Stephan Wach

Stephan Wach

13 6 2022

Packages/settings

Importing csv

Data adjustment

New var “total_count” for data excl.

Multi and practice as factors

New variable combining UVs

Data exclusion

Detecting possible outliers

Dataset names of Variables

Deskriptive statistics

DescribeBy

Summary

Histogramm age

Frequency tables groups

Mean/SD by groups/Variables

Total_count

AV1 recall_count

AV2 open.questions_count

AV3 transfer.question_count

Boxplots

ANOVA + Testing assumptions

ANOVA all AVs

Effect size

apaTables

Levene-Test all AV

Normal distribution of residuals

Interaction plot

AV1

AV2

AV3

Boxplots

AV1

AV2

AV3

Contrasts

Package lsmeans

Defining contrasts

AV1

AV2

AV3

H1 Equivalence test Spacing effect

Descriptive statistics AV1

H1-AV1

Descriptive statistics AV2

H1-AV2

Descriptive statistics AV3

H1-AV3

H2 Equivalence test Multimedia effect

Descriptive statistics AV1

H2-AV1

Descriptive statistics AV2

H2-AV2

Descriptive statistics AV3

H2-AV3

H3 Interaction

Descriptive statistics AV1

H3.1-AV1

Descriptive statistics AV2

H3.1-AV2

Descriptive statistics AV3

H3.1-AV3

Descriptive statistics AV1

H3.2-AV1

Descriptive statistics AV2

H3.2-AV2

Descriptive statistics AV3

H3.2-AV3